An amusement park sells child and adult tickets at a ratio of 8:1. On Saturday, they sold 147 more child tickets than adult tickets. How many tickets did the amusement park sell on... An amusement park sells child and adult tickets at a ratio of 8:1. On Saturday, they sold 147 more child tickets than adult tickets. How many tickets did the amusement park sell on Saturday? Read more

Steps to Solve

1. Define Variables for the Ticket Sales
   Let the number of adult tickets sold be represented by ( A ).
   Since the ratio of child tickets to adult tickets is ( 8:1 ), the number of child tickets sold can be represented as ( C = 8A ).

2. Set Up the Equation
   According to the problem, the amusement park sold 147 more child tickets than adult tickets. This gives us the equation:
   $$ C = A + 147 $$

3. Substitute Child Tickets into the Equation
   Now, substitute ( C ) with ( 8A ) in the equation:
   $$ 8A = A + 147 $$

4. Solve for Adult Tickets
   To isolate ( A ), subtract ( A ) from both sides of the equation:
   $$ 8A - A = 147 $$
   which simplifies to
   $$ 7A = 147 $$
   Now, divide both sides by 7:
   $$ A = \frac{147}{7} = 21 $$

5. Calculate Child Tickets
   Now that we have the number of adult tickets, substitute ( A ) back into the child tickets equation:
   $$ C = 8A = 8 \times 21 = 168 $$

6. Find the Total Tickets Sold
   Finally, add the number of child tickets and adult tickets to find the total:
   $$ \text{Total} = A + C = 21 + 168 = 189 $$